# MorphoActivation: Generalizing ReLU activation function by mathematical morphology

arXiv: https://arxiv.org/abs/2207.06413 · HTML: https://mlsanity.com/paper/2207.06413/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 36 references that are in the map.
- First posted on arXiv 13 Jul 2022.

## Builds on (most cited first, 6 of 6)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Maxout Networks](https://mlsanity.com/paper/1302.4389/) (2013)
- [Training BatchNorm and Only BatchNorm: On the Expressive Power of Random Features in CNNs](https://mlsanity.com/paper/2003.00152/) (2020)
- [Tropical Geometry of Deep Neural Networks](https://mlsanity.com/paper/1805.07091/) (2018)
- [Activate or Not: Learning Customized Activation](https://mlsanity.com/paper/2009.04759/) (2020)
- [Reduced Dilation-Erosion Perceptron for Binary Classification](https://mlsanity.com/paper/2003.02306/) (2020)

## Built on by (most cited first, 3 of 3)

- [Tight Certified Robustness via Min-Max Representations of ReLU Neural Networks](https://mlsanity.com/paper/2310.04916/) (2023)
- [Training Deep Morphological Neural Networks as Universal Approximators](https://mlsanity.com/paper/2505.09710/) (2025)
- [HaarNet: Large-scale Linear-Morphological Hybrid Network for RGB-D Semantic Segmentation](https://mlsanity.com/paper/2310.07669/) (2023)

## Abstract (arXiv)

This paper analyses both nonlinear activation functions and spatial max-pooling for Deep Convolutional Neural Networks (DCNNs) by means of the algebraic basis of mathematical morphology. Additionally, a general family of activation functions is proposed by considering both max-pooling and nonlinear operators in the context of morphological representations. Experimental section validates the goodness of our approach on classical benchmarks for supervised learning by DCNN.